\[ \begin{array}{r} 2 e^{x}-3=1 \\ 2 e^{x}=4 \\ e^{x}=2 \end{array} \] What is the next step when solving the equation $2 \mathrm{e}^{\mathrm{x}}-3=1$ ?

Step 1 ：The next step in solving the equation \(2e^x - 3 = 1\) is to add \(3\) to both sides of the equation to get \(2e^x = 4\).

Step 2 ：Then, divide both sides of the equation by \(2\) to isolate \(e^x\), which gives \(e^x = 2\).

Step 3 ：Finally, take the natural logarithm of both sides to solve for \(x\), which gives \(x = \ln(2)\).

Step 4 ：\(\boxed{x = \ln(2)}\)